Option theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Chichester [u.a.]
Wiley
2005
|
| Ausgabe: | Transferred to digital print. |
| Schriftenreihe: | Wiley finance series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 371 S. graph. Darst. |
| ISBN: | 0471492892 |
Internformat
MARC
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| 100 | 1 | |a James, Peter |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Option theory |c Peter James |
| 250 | |a Transferred to digital print. | ||
| 264 | 1 | |a Chichester [u.a.] |b Wiley |c 2005 | |
| 300 | |a XI, 371 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-016274366 | ||
Datensatz im Suchindex
| _version_ | 1804137314520137728 |
|---|---|
| adam_text | Contents
Preface
xiii
PART
1
ELEMENTS OF OPTION THEORY
1
3
3
7
8
11
15
15
16
18
20
22
26
29
29
30
33
34
35
35
38
44
46
48
Fundamentals
1.1
Conventions
1.2
Arbitrage
1.3
Forward contracts
1.4
Futures contracts
Option Basics
2.1
Payoffs
2.2
Option prices before maturity
2.3
American options
2.4
Put-call parity for
american
options
2.5
Combinations of options
2.6
Combinations before maturity
Stock Price Distribution
3.1
Stock price movements
3.2
Properties of stock price distribution
3.3
Infinitesimal price movements
3.4
Ito s lemma
Principles of Option Pricing
4.1
Simple example
4.2
Continuous time analysis
4.3
Dynamic hedging
4.4
Examples of dynamic hedging
4.5
Greeks
___________________________Contents_________________________________
5 The Black Scholes Model 51
5.1
Introduction
51
5.2
Derivation of model from expected values
51
5.3
Solutions of the Black Scholes equation
52
5.4
Greeks for the Black Scholes model
53
5.5
Adaptation to different markets
56
5.6
Options on forwards and futures
58
6
American Options
63
6.1
Black Scholes equation revisited
63
6.2
Barone-Adesi and Whaley approximation
65
6.3
Perpetual puts
68
6.4
American options on futures and forwards
69
PART
2
NUMERICAL METHODS
73
7
The Binomial Model
75
7.1
Random walk and the binomial model
75
7.2
The binomial network
77
7.3
Applications
80
8
Numerical Solutions of the Black Scholes Equation
87
8.1
Finite difference approximations
87
89
91
93
97
100
105
105
109
113
115
118
123
10
Monte
Cario
125
10.1
Approaches to option pricing
125
10.2
Basic Monte Carlo method
127
10.3
Random numbers
130
10.4
Practical applications
133
10.5
Quasi-random numbers
135
10.6
Examples
139
8.2
Conditions for satisfactory solutions
8.3
Explicit finite difference method
8.4
Implicit finite difference methods
8.5
A worked example
8.6
Comparison of methods
9
Variable Volatility
9.1
Introduction
9.2
Local volatility and the
Fokker
Planck equation
9.3
Forward induction
9.4
Trinomial trees
9.5
Derman
Kani
implied trees
9.6
Volatility surfaces
vtu
Contents
PART
3
APPLICATIONS: EXOTIC OPTIONS
143
11
Simple Exotics
145
145
147
148
149
151
Simple Exotics
11.1
Forward start options
11.2
Choosers
11.3
Shout options
11.4
Binary (digital) options
11.5
Power options
Two Asset Options
12.1
Exchange options
(Margrabe)
12.2
Maximum of two assets
12.3
Maximum of three assets
12.4
Rainbow options
12.5
Black Scholes equation for two assets
12.6
Binomial model for two asset options
12
Two Asset Options
153
153
155
156
158
158
160
13
Currency Translated Options
163
13.1
Introduction
163
13.2
Domestic currency strike (compo)
163
13.3
Foreign currency strike: fixed exchange rate
(quanto)
165
13.4
Some practical considerations
167
14
Options on One Asset at Two Points in Time
169
14.1
Options on options (compound options)
169
14.2
Complex choosers
173
14.3
Extendible options
173
15
Barriers: Simple European Options
177
15.1
Single barrier calls and puts
177
15.2
General expressions for single barrier options
180
15.3
Solutions of the Black Scholes equation
181
15.4
Transition probabilities and rebates
182
15.5
Binary (digital) options with barriers
183
15.6
Common applications
184
15.7
Greeks
186
15.8
Static hedging
187
16
Barriers: Advanced Options
189
16.1
Two barrier options
189
16.2
Outside barrier options
190
16.3
Partial barrier options
192
16.4
Lookback
options
193
16.5
Barrier options and trees
195
ix
Contents
17
Asian Options
201
17.1
Introduction
201
17.2
Geometric average price options
203
17.3
Geometric average strike options
206
17.4
Arithmetic average options:
lognormal
solutions
206
17.5
Arithmetic average options: Edgeworth expansion
209
17.6
Arithmetic average options: geometric conditioning
211
17.7
Comparison of methods
215
18
Passport Options
217
18.1
Option on an investment strategy (trading option)
217
18.2
Option on an optimal investment strategy (passport option)
220
18.3
Pricing a passport option
222
PART
4
STOCHASTIC THEORY
225
19
Arbitrage
227
19.1
Simplest model
227
19.2
The arbitrage theorem
229
19.3
Arbitrage in the simple model
230
20
Discrete Time Models
233
20.1
Essential jargon
233
20.2
Expectations
234
20.3
Conditional expectations applied to the one-step model
235
20.4
Multistep model
237
20.5
Portfolios
238
20.6
First approach to continuous time
240
21
Brownian Motion
243
21.1
Basic properties
243
21.2
First and second variation of analytical functions
245
2L3 First and second variation of Brownian motion
246
22
Transition to Continuous Time
249
22.1
Towards a new calculus
249
22.2
Ito
integrals
252
22.3
Discrete model extended to continuous time
255
23
Stochastic Calculus
259
23.1
Introduction
259
23.2
Ito s transformation formula (Ito s lemma)
260
23.3
Stochastic integration
261
23.4
Stochastic differential equations
262
23.5
Partial differential equations
265
23.6
Local time
266
________________________________Contents________________________________
23.7
Results for two dimensions
269
23.8
Stochastic control
271
24
Equivalent Measures
275
24.1
Change of measure in discrete time
275
24.2
Change of measure in continuous time: Girsanov s theorem
277
24.3
Black Scholes analysis
280
25
Axiomatic Option Theory
283
25.1
Classical vs. axiomatic option theory
283
25.2
American options
284
25.3
The stop—go option paradox
287
25.4
Barrier options
290
25.5
Foreign currencies
293
25.6
Passport options
297
Mathematical Appendix
299
A.
1
Distributions and integrals
299
A.2 Random walk
309
A.3 The Kolmogorov equations
314
A.4 Partial differential equations
318
A.5 Fourier methods for solving the heat equation
322
A.6 Specific solutions of the heat equation (Fourier methods)
325
A.7 Green s functions
329
A.8
Fokker
Planck equations with absorbing barriers
336
A.9 Numerical solutions of the heat equation
344
A.
10
Solution of finite difference equations by
LU
decomposition
347
A.
11
Cubic spline
349
A.
12
Algebraic results
351
A.
13
Moments of the arithmetic mean
353
A.
14
Edgeworth expansions
356
Bibliography and References
361
Commentary
361
Books
363
Papers
364
Index
367
Xl
|
| adam_txt |
Contents
Preface
xiii
PART
1
ELEMENTS OF OPTION THEORY
1
3
3
7
8
11
15
15
16
18
20
22
26
29
29
30
33
34
35
35
38
44
46
48
Fundamentals
1.1
Conventions
1.2
Arbitrage
1.3
Forward contracts
1.4
Futures contracts
Option Basics
2.1
Payoffs
2.2
Option prices before maturity
2.3
American options
2.4
Put-call parity for
american
options
2.5
Combinations of options
2.6
Combinations before maturity
Stock Price Distribution
3.1
Stock price movements
3.2
Properties of stock price distribution
3.3
Infinitesimal price movements
3.4
Ito's lemma
Principles of Option Pricing
4.1
Simple example
4.2
Continuous time analysis
4.3
Dynamic hedging
4.4
Examples of dynamic hedging
4.5
Greeks
_Contents_
5 The Black Scholes Model 51
5.1
Introduction
51
5.2
Derivation of model from expected values
51
5.3
Solutions of the Black Scholes equation
52
5.4
Greeks for the Black Scholes model
53
5.5
Adaptation to different markets
56
5.6
Options on forwards and futures
58
6
American Options
63
6.1
Black Scholes equation revisited
63
6.2
Barone-Adesi and Whaley approximation
65
6.3
Perpetual puts
68
6.4
American options on futures and forwards
69
PART
2
NUMERICAL METHODS
73
7
The Binomial Model
75
7.1
Random walk and the binomial model
75
7.2
The binomial network
77
7.3
Applications
80
8
Numerical Solutions of the Black Scholes Equation
87
8.1
Finite difference approximations
87
89
91
93
97
100
105
105
109
113
115
118
123
10
Monte
Cario
125
10.1
Approaches to option pricing
125
10.2
Basic Monte Carlo method
127
10.3
Random numbers
130
10.4
Practical applications
133
10.5
Quasi-random numbers
135
10.6
Examples
139
8.2
Conditions for satisfactory solutions
8.3
Explicit finite difference method
8.4
Implicit finite difference methods
8.5
A worked example
8.6
Comparison of methods
9
Variable Volatility
9.1
Introduction
9.2
Local volatility and the
Fokker
Planck equation
9.3
Forward induction
9.4
Trinomial trees
9.5
Derman
Kani
implied trees
9.6
Volatility surfaces
vtu
Contents
PART
3
APPLICATIONS: EXOTIC OPTIONS
143
11
Simple Exotics
145
145
147
148
149
151
Simple Exotics
11.1
Forward start options
11.2
Choosers
11.3
Shout options
11.4
Binary (digital) options
11.5
Power options
Two Asset Options
12.1
Exchange options
(Margrabe)
12.2
Maximum of two assets
12.3
Maximum of three assets
12.4
Rainbow options
12.5
Black Scholes equation for two assets
12.6
Binomial model for two asset options
12
Two Asset Options
153
153
155
156
158
158
160
13
Currency Translated Options
163
13.1
Introduction
163
13.2
Domestic currency strike (compo)
163
13.3
Foreign currency strike: fixed exchange rate
(quanto)
165
13.4
Some practical considerations
167
14
Options on One Asset at Two Points in Time
169
14.1
Options on options (compound options)
169
14.2
Complex choosers
173
14.3
Extendible options
173
15
Barriers: Simple European Options
177
15.1
Single barrier calls and puts
177
15.2
General expressions for single barrier options
180
15.3
Solutions of the Black Scholes equation
181
15.4
Transition probabilities and rebates
182
15.5
Binary (digital) options with barriers
183
15.6
Common applications
184
15.7
Greeks
186
15.8
Static hedging
187
16
Barriers: Advanced Options
189
16.1
Two barrier options
189
16.2
Outside barrier options
190
16.3
Partial barrier options
192
16.4
Lookback
options
193
16.5
Barrier options and trees
195
ix
Contents
17
Asian Options
201
17.1
Introduction
201
17.2
Geometric average price options
203
17.3
Geometric average strike options
206
17.4
Arithmetic average options:
lognormal
solutions
206
17.5
Arithmetic average options: Edgeworth expansion
209
17.6
Arithmetic average options: geometric conditioning
211
17.7
Comparison of methods
215
18
Passport Options
217
18.1
Option on an investment strategy (trading option)
217
18.2
Option on an optimal investment strategy (passport option)
220
18.3
Pricing a passport option
222
PART
4
STOCHASTIC THEORY
225
19
Arbitrage
227
19.1
Simplest model
227
19.2
The arbitrage theorem
229
19.3
Arbitrage in the simple model
230
20
Discrete Time Models
233
20.1
Essential jargon
233
20.2
Expectations
234
20.3
Conditional expectations applied to the one-step model
235
20.4
Multistep model
237
20.5
Portfolios
238
20.6
First approach to continuous time
240
21
Brownian Motion
243
21.1
Basic properties
243
21.2
First and second variation of analytical functions
245
2L3 First and second variation of Brownian motion
246
22
Transition to Continuous Time
249
22.1
Towards a new calculus
249
22.2
Ito
integrals
252
22.3
Discrete model extended to continuous time
255
23
Stochastic Calculus
259
23.1
Introduction
259
23.2
Ito's transformation formula (Ito's lemma)
260
23.3
Stochastic integration
261
23.4
Stochastic differential equations
262
23.5
Partial differential equations
265
23.6
Local time
266
_Contents_
23.7
Results for two dimensions
269
23.8
Stochastic control
271
24
Equivalent Measures
275
24.1
Change of measure in discrete time
275
24.2
Change of measure in continuous time: Girsanov's theorem
277
24.3
Black Scholes analysis
280
25
Axiomatic Option Theory
283
25.1
Classical vs. axiomatic option theory
283
25.2
American options
284
25.3
The stop—go option paradox
287
25.4
Barrier options
290
25.5
Foreign currencies
293
25.6
Passport options
297
Mathematical Appendix
299
A.
1
Distributions and integrals
299
A.2 Random walk
309
A.3 The Kolmogorov equations
314
A.4 Partial differential equations
318
A.5 Fourier methods for solving the heat equation
322
A.6 Specific solutions of the heat equation (Fourier methods)
325
A.7 Green's functions
329
A.8
Fokker
Planck equations with absorbing barriers
336
A.9 Numerical solutions of the heat equation
344
A.
10
Solution of finite difference equations by
LU
decomposition
347
A.
11
Cubic spline
349
A.
12
Algebraic results
351
A.
13
Moments of the arithmetic mean
353
A.
14
Edgeworth expansions
356
Bibliography and References
361
Commentary
361
Books
363
Papers
364
Index
367
Xl |
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| illustrated | Illustrated |
| index_date | 2024-07-02T19:33:08Z |
| indexdate | 2024-07-09T21:10:20Z |
| institution | BVB |
| isbn | 0471492892 |
| language | English |
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| spelling | James, Peter Verfasser aut Option theory Peter James Transferred to digital print. Chichester [u.a.] Wiley 2005 XI, 371 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley finance series Optionspreistheorie (DE-588)4135346-8 gnd rswk-swf Optionspreistheorie (DE-588)4135346-8 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016274366&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | James, Peter Option theory Optionspreistheorie (DE-588)4135346-8 gnd |
| subject_GND | (DE-588)4135346-8 |
| title | Option theory |
| title_auth | Option theory |
| title_exact_search | Option theory |
| title_exact_search_txtP | Option theory |
| title_full | Option theory Peter James |
| title_fullStr | Option theory Peter James |
| title_full_unstemmed | Option theory Peter James |
| title_short | Option theory |
| title_sort | option theory |
| topic | Optionspreistheorie (DE-588)4135346-8 gnd |
| topic_facet | Optionspreistheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016274366&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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